The idea that interactions between species matter goes all the way back to the origins of evolutionary biology in the writing of Charles Darwin:

What a struggle between the several kinds of trees must here have gone on during long centuries, each annually scattering its seeds by the thousand; what war between insect and insect – between insects, snails, and other animals with birds and beasts of prey – all striving to increase, and all feeding on each other or on the trees or their seeds and seedlings, or on the other plants which first clothed the ground and thus checked the growth of the trees! (On the Origin of Species, 1859: 74-5)

This image of constant struggle among living things was more formally encapsulated in a 1973 paper by Leigh Van Valen (which paper is not, alas, available online), who proposed that constant coevolution with other species should mean that natural populations of living things are constantly adapting – in response to competitors, mutualists, predators, parasites – without gaining ground in the struggle, because the other species are also adapting. Van Valen lifted an image from Lewis Carroll's Through the Looking-Glass, in which the Red Queen tells Alice that, in the strange world of Looking-Glass Land, "... it takes all the running you can do, to keep in the same place."

They were running hand in hand, and the Queen went so fast that it was all she could do to keep up with her ... The most curious part of the thing was, that the trees and the other things around them never seemed to changed their places at all.

"... it takes all the running you can do, to keep in the same place." Image from Through the Looking-Glass, via VictorianWeb.

Thus, this idea that fuels much of my research, and a great deal of scientific study over the last three decades, is often identified with the Red Queen. What is interesting about this result is that Van Valen wasn't interested in species interactions as such; he was trying to explain a pattern in the fossil record – that, for a wide variety of living things, the probability that a species would go extinct was independent of its age. That is, species that have been around for ten million years are no better adapted to their environments than species that have just formed; the probability of extinction is constant.

Van Valen's explanation for this result was that something must constantly act to prevent living things from becoming better adapted, and better able to resist extinction, over time – specifically, the Red Queen's race against other living things. Whenever a species "loses" the race, it goes extinct, regardless of how long the race has been up to that point. A similar pattern applies to the creation of new species – if coevolutionary interactions often help create reproductive isolation, then new species should also form at a roughly constant rate [$a]. Since this is what we observe, many biologists conclude that coevolution is responsible for the diversity of life on Earth.

What if the race doesn't matter?

Fortunately for the advance of knowledge, however, not all evolutionary biologists have the same perspective. Paleontologists, for instance, tend to think that the year-to-year dynamics of the Red Queen race don't make much difference in the longer run, over millions of years. They'd argue that most of the evolutionary change induced by coevolution between species is too variable and fleeting to have much effect on the rates at which species are formed and go extinct. Under this view, random geological events – continents splitting, mountain ranges rising, volcanoes erupting – are more likely to create new species and force them to extinction.

What matters more in the history of life, the biological environment, or the physical environment? Photos by Martin Heigan and Cedric Favero.

This competing model should also lead to a roughly constant rate of species formation and extinction, but it predicts a different pattern of variation around that constant rate than the coevolutionary Red Queen does. If most speciation and extinction events are caused by coevolution, then the time periods between speciation events should follow a normal distribution – forming a "bell curve" with most periods close to the average length, and symmetrical tails of longer and shorter periods of time. On the other hand, if many different, individually rare geological events are the most common cause of speciation and extinction, the periods between speciation events should follow an exponential distribution, with most periods being shorter than the average, but a long tail of longer periods as well.

This contrast is the crux of a study recently published in Nature. The paper's authors, Venditti et al., examined 101 evolutionary trees estimated from genetic data, including groups like the dog family, roses, and bees. For each group's evolutionary tree, they determined the distribution of the lengths of time periods between speciation events. A majority of the trees – 78% – supported the exponential model. That is, 78% of the groups of organisms examined had evolved and diversified in a fashion best explained by geology, not coevolution. None of the groups fit the normal distribution, and only 8% fit the related lognormal distribution.

The Red Queen is dead, long live the Red Queen!

This result suggests that within many groups of organisms, the physical environment is a more common cause of reproductive isolation or extinction than the biological environment. However, this isn't to say that species interactions don't matter. As Van Valen originally noted, extinction rates may be roughly constant within large groups of organisms, like those examined by Venditti et al., but those constant rates vary from group to group. These differences in rate may still depend on species interactions, because species interactions can shape how prone a population is to reproductive isolation.

For instance, a group of plants that has lousy seed dispersers may form new species in response to much smaller, and more common, geological barriers than a group of plants whose seeds can travel for hundreds of miles. Additionally, species interactions that promote diversity within the interacting species may mean that when geology creates isolation, the resultant daughter species are more different from each other than they would otherwise be, and less likely to re-merge if they come into contact again. Under that scenario, speciation caused by the physical environment would act to preserve variation [$a] created by the biological environment.

So, perhaps the Red Queen doesn't operate the way we thought she did, with constant coevolutionary races spinning off new species and killing off others. But that hardly means that Red Queen processes don't matter in the long run.

"...If these factors have the potential on their own to cause a speciation, the branch length distribution will follow an exponential density, that being the waiting time between successive events of a Poisson process. This is also the density that arises if there is a constant probability of speciation."

So the red queen predicts a constant probability of speciation, which generates an exponential distribution, and the many rare but important factors model predicts an exponential distribution, how can the authors conclude anything other than that the exponential is generally a good fit?

My other question is, do you have any idea how the red queen could actually lead to speciation? extinction makes some sense in that, if you lose the race, you die. But speciation? It doesn't seem to follow that if you win the race, you speciate. Speciation is not the opposite of extinction in terms of population processes. I suppose I should just look up the reference...

Ok, lastly, I happen to think that the many rare powerful events model is super-intuitive, but do we have any idea how often single events really cause speciation? It almost seems like, however you define a species, multiple events must cause speciation. Even in geographic isolation, without substantial genetic change, likely owing to biotic interactions, reproductive isolation is unlikely to accrue... or without some reduction in gene flow, local adaptation is unlikely to result in speciation.

Sorry for the "attack", we just read this paper for lab meeting a couple weeks back, and it got me all pumped.

So, I think part of what you're identifying is a conflation between the Red Queen processes (constant arms-race-style coevolution) and the pattern they were proposed to explain (constant rates of extinction/speciation). Technically speaking, all the models tested by Venditti et al. conform to the Red Queen pattern of constant extinction/speciation rates -- they vary in the distribution around that rate, and it's the distributions that are associated with different explanatory processes.

As the text you quote indicates, the exponential distribution arises when stochastic events are each individually capable of causing speciation; the normal (or lognormal) distribution arises when many events contribute additively (or multiplicatively) to causing speciation. I follow Benton's commentary in understanding that speciation due to coevolution would actually be composed of many different interacting events (coevolution with parasites + sexual selection + local adaptation to a mutualist &c), which means that it's associated with the normal distribution – but this is a point where you could certainly disagree.

But so my point is that Venditti et al. are both confirming the Red Queen pattern, and arguing that it arises for reasons other than the classic Red Queen processes.

For ways that Red Queen processes could lead to speciation, the best discussion is probably in the literature associated with Thompson's "geographic mosaic of coevolution" theory. The idea (as I understand it) is that arms races across spatially structured populations can get out of sync, and that can create reproductive isolation. I personally am not at all sure that arms races should do this, as you might recall from my presentation at the last Evolution meetings.

Finally, I think that hard-core allopatric speciation people would tell you that drift in isolation is enough to create genetic incompatibilities – that, as long as the geographic barrier stays in place long enough, you'll inevitably end up with separate species. I think that probably does happen, but I'd agree that it happens faster if you've also got differential selection on your geographically isolated populations. So this is another point I think you can legitimately argue with in Venditti et al.

I'm not sure I follow you. I am fairly certain that normally distributed branch lengths are not consistent with a constant rate model. Normally distributed branch lengths imply that the probability of speciation is time-dependent because the many small factors need time to accumulate, whereas constant rates always produce something related to the exponential, no? I realize the commentary explicitly states that the red queen predicts normally distributed branch lengths, but the authors never state this in any clear way, and I think I disagree. This may be my statistical naivete, but I blame the authors for the confusion. A table of predictions and biological interpretations from the hypotheses would have been nice. I do have one positive, non-nitpicky thing to say... at least this gives pretty strong justification to using an exponential branch-length prior in mrbayes!

So, I'll admit up front that, while reading Venditti et al., figuring out how each distribution model corresponds to each causal process was far and away the hardest part, and I may still not really understand what's going on. It's really a prime example of how writing for S/Nature can sacrifice clarity for brevity.

But: I don't really understand how the normal distribution implies time-dependent probability of speciation. If the "many small factors" are due to coevolutionary cycling, they wouldn't accumulate over time, but fluctuate – so you get speciation when several different factors happen to favor it simultaneously. I'm picturing it (maybe wrongly) as multiple waves with different wavelengths, superimposed so that sometimes peaks overlap and reinforce each other. I don't know any reason why that would become more probable over time.

More directly, I can't wrap my head around how a tree with normally-distributed branch lengths would end up with more species arising most recently – which is what you get, I think, if the probability of speciation increases over time. And in any event, time-dependent speciation is explicitly not the Red Queen pattern, so I don't know why anyone would associate it with Red Queen processes.

Heh. It's about time I took up bellicose residence in the comment section of somebody's blog.

ok, so in the paper, I interpret the statement that the red queen produces a constant rate of speciation to mean that it occurs according to a poisson process. a poisson process produces exponentially distributed waiting times (i.e. branch lengths). because the rare-but-sufficient model also produces exponentially distributed branch lengths, these should be causally indistinguishable based the distribution. this is according to omniscient wikipedia. so I think what that means is that to actually produce normally distributed branch lengths, the many small factors have to accumulate randomly over time without being reset, otherwise you have a constant probability. this would suggest that the probability of speciation along any one branch increases with time, right? I'm not saying that the probability of speciation changes over the life of the clade, just the life of any one branch. The paper says the weibull distribution is the one that accounts for changing probability of speciation along a branch over time, but wikipedia describes the exponential and geometric distributions as the only "memoryless" probability distributions (i.e. the only ones for which the probability of an event occurring are independent of how long it has been since the last event occurred).

I agree with your description of coevolutionary cycling, but I think that produces a constant probability, and therefore exponential branch lengths. If the many small events have to coincide instead of accumulate, I think you are still basically looking at a constant probability of one rare event occurring.

As for the normal producing mostly species that arose recently, I don't know. I'm not sure testing a distribution of internal branch lengths stripped from a phylogeny can really account for how those branches are distributed on the tree. ugh, this is confusing, but I am pretty interested in getting it sorted out.

OK, here's another stab at it, with all previous caveats in mind: I'm with you that the RQ implies Poisson-distributed speciation events - but we're talking about the distribution of times between speciation events. Venditti et al. explicitly say that "rare-but-sufficient" events should lead to exponentially distributed branch lengths, and have a citation to support it (Gillespie 1991, which is searchable on Google Books). So, fine. They don't have a citation (or derivation in the SI) for the alternative, that "many small events acting additively" lead to normally distributed branch lengths. So, I think that leaves two options:

1. Maybe if your Poisson-distributed events have a high enough frequency – or if you add together many different Poisson-distributed events – you end up with normally-distributed times between events, instead of exponentially-distributed ones?

2. Maybe the normal distribution of branch lengths doesn't arise from any model with a constant rate of speciation. In which case, Venditti et al. have pulled a sleight-of-hand by asserting that the RQ process leads to a non-RQ pattern, without showing why.

I'm really just thinking out loud at this point. Dammit, Noah, why can't you just let me pontificate about flashy results without worrying about the substance of the paper?

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